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Nonparametric Estimation of the Ruin Probability in the Classical Compound Poisson Risk Model

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  • Yuan Gao

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
    These authors contributed equally to this work.)

  • Lingju Chen

    (College of Mathematics and Data Science, Minjiang University, Fuzhou 350108, China
    These authors contributed equally to this work.)

  • Jiancheng Jiang

    (Department of Mathematics and Statistics, School of Data Science, University of North Carolina, Charlotte, NC 28223, USA
    These authors contributed equally to this work.)

  • Honglong You

    (School of Statistics, Qufu Normal University, Qufu 273165, China
    These authors contributed equally to this work.)

Abstract

In this paper we study estimating ruin probability which is an important problem in insurance. Our work is developed upon the existing nonparametric estimation method for the ruin probability in the classical risk model, which employs the Fourier transform but requires smoothing on the density of the sizes of claims. We propose a nonparametric estimation approach which does not involve smoothing and thus is free of the bandwidth choice. Compared with the Fourier-transformation-based estimators, our estimators have simpler forms and thus are easier to calculate. We establish asymptotic distributions of our estimators, which allows us to consistently estimate the asymptotic variances of our estimators with the plug-in principle and enables interval estimates of the ruin probability.

Suggested Citation

  • Yuan Gao & Lingju Chen & Jiancheng Jiang & Honglong You, 2020. "Nonparametric Estimation of the Ruin Probability in the Classical Compound Poisson Risk Model," JRFM, MDPI, vol. 13(12), pages 1-12, November.
    • Handle: RePEc:gam:jjrfmx:v:13:y:2020:i:12:p:298-:d:453207
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    References listed on IDEAS

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    1. S. Pitts, 1994. "Nonparametric estimation of compound distributions with applications in insurance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(3), pages 537-555, September.
    2. Landriault, David & Willmot, Gordon, 2008. "On the Gerber-Shiu discounted penalty function in the Sparre Andersen model with an arbitrary interclaim time distribution," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 600-608, April.
    3. Baumgartner, Benjamin & Gatto, Riccardo, 2010. "A Bootstrap Test for the Probability of Ruin in the Compound Poisson Risk Process," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 241-255, May.
    4. Cai, Jun & Wu, Yanhong, 1997. "Some improvements on the Lundberg bound for the ruin probability," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 395-403, May.
    5. Frees, Edward W., 1986. "Nonparametric Estimation of the Probability of Ruin," ASTIN Bulletin, Cambridge University Press, vol. 16(S1), pages 81-90, April.
    6. You, Honglong & Guo, Junyi & Jiang, Jiancheng, 2020. "Interval estimation of the ruin probability in the classical compound Poisson risk model," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    7. Croux, Kristof & Veraverbeke, Noel, 1990. "Nonparametric estimators for the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 9(2-3), pages 127-130, September.
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    Cited by:

    1. Xie, Jiayi & Zhang, Zhimin, 2020. "Statistical estimation for some dividend problems under the compound Poisson risk model," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 101-115.
    2. Yuan Gao & Honglong You, 2021. "The Speed of Convergence of the Threshold Estimator of Ruin Probability under the Tempered α -Stable Lévy Subordinator," Mathematics, MDPI, vol. 9(21), pages 1-9, October.
    3. Kang Hu & Ya Huang & Yingchun Deng, 2023. "Estimating the Gerber–Shiu Function in the Two-Sided Jumps Risk Model by Laguerre Series Expansion," Mathematics, MDPI, vol. 11(9), pages 1-30, April.
    4. Wen Su & Yunyun Wang, 2021. "Estimating the Gerber-Shiu Function in Lévy Insurance Risk Model by Fourier-Cosine Series Expansion," Mathematics, MDPI, vol. 9(12), pages 1-18, June.

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